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Donald Trump commits to the Republican party

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Washington (CNN)Donald Trump committed Tuesday to not running for president as an independent -- an idea he has floated in the past -- during the CNN hosted Republican debate.

Trump said Thursday that he is "totally committed to the Republican Party" and said he feels "very honored to be the front-runner" after he was asked whether he was ready to commit to not running as a third-party candidate.

Trump said that he has "gained great respect for the Republican leadership" in recent weeks as well as his fellow Republican candidates for president.

Just last week, Trump floated the possibility of launching a third party bid. Republicans -- including the Republican National Committee Chairman Reince Priebus -- roundly criticized his proposal to bar all foreign Muslims from entering the United States.

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As if firing a warning shot, Trump last week tweeted the results of a poll that showed that two-thirds of his supporters would vote for him should he leave the Republican Party and pursue an independent bid.

A new poll indicates that 68% of my supporters would vote for me if I departed the GOP & ran as an independent. https://t.co/ztP5d2ctZl

Trump signed a loyalty pledge to the Republican Party in September -- vowing to support the Republican nominee and not run as an independent -- but has since insisted that that pledge was contingent on the GOP treating him "fairly."

Asked by CNN's Chris Cuomo after the debate if his pledge to remain in the GOP race meant "no exceptions, Trump confirmed.

"I'm going to be a Republican, I'm not going to be doing a third party," Trump said. "No matter what."